Consider a glass of 277 mL of water at 25°C. Calculate the mass of ice at -15°C that must be added to cool the water to 10°C after thermal equilibrium is achieved. To find the mass of water use the density of water = 1.0 g/mL.

I have no idea how to start this. I guess i hae to first find the grams of water there are. I have the values of the Cs of ice and DeltaH of fusion.

q to move ice from -15 to zero C.

q1 = mass ice x specific heat ice x (Tfinal-Tinitial) [Note: Be careful that you keep the signs ok here. Tfinal = 0 and Tinitial = -15; therefore, Tf-Ti = +15.

q2 = heat to melt ice
q2 = mass ice x heat fusion

q3 = heat to move melting ice from zero C to 10 C.
q3 = mass x specific heat water x (Tfinal-Tinitial)

q4 = heat lost in moving 277 mL water from 25 to 10
q4 = mass x specific heat x (Tfinal-Tinitial)
Now add q1 + q2 + q3 + q4 = 0.
mass ice = x and mass melted ice = x. Solve for x. I get something close to 40 grams.

To solve this problem, we need to follow a few steps:

Step 1: Find the mass of water in grams
Given that the volume of water is 277 mL and the density of water is 1.0 g/mL, we can calculate the mass of water using the formula:

Mass of water = Volume of water × Density of water

Mass of water = 277 mL × 1.0 g/mL

Step 2: Calculate the heat lost by the water
The amount of heat lost by the water can be determined using the formula:

Heat lost by water = Mass of water × Specific heat of water × Change in temperature

The specific heat capacity of water is approximately 4.18 J/g°C.
In this case, the change in temperature is 25°C - 10°C = 15°C.

Step 3: Calculate the heat gained by the ice
The heat gained by the ice can be determined using the formula:

Heat gained by ice = Mass of ice × Specific heat of ice × Change in temperature

The specific heat capacity of ice is approximately 2.09 J/g°C.
In this case, the change in temperature is 10°C - (-15°C) = 25°C.

Step 4: Equate the heat lost by the water to the heat gained by the ice
Since heat is conserved in a closed system, the heat lost by the water is equal to the heat gained by the ice:

Heat lost by water = Heat gained by ice

Mass of water × Specific heat of water × Change in temperature = Mass of ice × Specific heat of ice × Change in temperature

Step 5: Solve for the mass of ice
Canceling out the common terms, we find:

Mass of water × Specific heat of water = Mass of ice × Specific heat of ice

Mass of ice = (Mass of water × Specific heat of water) / Specific heat of ice

Substituting the values:

Mass of ice = (Mass of water × 4.18 J/g°C) / 2.09 J/g°C

Hope this helps in understanding the approach to solving the problem!